Name _______________________________

The Sidereal Period of the Moon

Print out this page and complete the exercise.

Objective: To determine the sidereal period of the moon by simple
means.

Theory:
The amount of time it takes the moon to orbit the Earth and appear
at the same place on the Celestial Sphere is called the sidereal
period of the moon. This amount of time is not the same
as the lunar month. The lunar month is the amount of time
between successive new moons, or full moons, or any two successive,
similar phases. Phases of the moon, however, depend on the relative
positions of the Earth, moon, and Sun. Since the Earth is orbiting
the Sun, these alignments occur at different absolute places in
the moon's orbit each month.

Figure 1

The diagram in figure 1 may help explain the difference between
the lunar (also called the synodic) period and the sidereal period.
At new moon number one (position A) we mark the position of the
Sun (or moon since they are the same) on the sky. Imagine that
a bright star is in the same line of sight. Notice that because
of the Earth's orbital motion, when the moon lines up with that
star the next month (position B), it is not yet new moon (position
C). From A around the moon's orbit to B is the sidereal period
(think with respect to the stars), while from A all the
way to C is the synodic period.

We intend to measure the sidereal period of the moon by noting
how the moon moves with respect to a nearby star. From night to
night the moon moves roughly 13° toward the east. This causes
the moon to rise roughly 52 minutes later each day. These are
average values, however, which are useful in judging when you
have to observe. The observations are best obtained near the first
quarter moon, when the moon is visible in the early evening sky.
First quarter moon occurs on 19 October. Observations near the
full moon are more difficult since the moonlight washes out the
sky. Full moon occurs on 26 October. Prime observing time then
is now until 24 October.

Imagine that on night one we find a bright star near the moon
as in figure 2. On the second night the situation is like figure
3.

Figure 2

Figure 3

Let us assume that the two measurements were made 24 hours apart
for simplicity. We can set up a ratio to tell us how long it takes
the moon to return to the position of figure 2. Notice that in
the 24 hours the moon moved 12°. Then

time for 360° = (1 day)*360°/12°= 30 days

More generally,

Sidereal period = (Elapsed Time)*360°/(Change in
angle)

Procedure:

We would like to measure the angular separation between the moon
and a bright star on two consecutive nights. Use your crosstaff
for these angular measurements. If clouds interfere on night two,
you can use a time interval of two days, but do not extend beyond
that.

1. Calendar Date ______________ Time ____________

Sky conditions __________________________________

Lunar phase ______________

Find a reasonably bright star near the moon and the ecliptic
and measure its separation from the moon. Try to measure from
the star to the center of the moon. The star can fall on either
side (east or west) of the moon. Place the moon as accurately
as you can on the SC-1 constellation chart. Copy this portion
of the chart as well as the position of the moon onto a blank
sheet of paper. Label enough stars so that it is clear where you
are. Measure the angular separation using the angular scales on
the SC-1.

Identify your star ______________

Angular separation using crosstaff _____________

Angular separation using SC-1 ___________

2. Calendar Date ______________ Time ____________

Sky conditions __________________________________

Lunar phase ______________

Identify the same star you used on night one, measure its angular
separation from the moon, transfer its position to the SC-1, then
to you sheet of paper, and measure its angular separation on the
sheet of paper.